I like to consider ∆S the result of a smoothing operation over energy differentials.
You can put work into a system to reestablish an energy differential. It just necessitates obtaining that other energy differential with which to do the work.
> I don't like that definition.
Physics isn't a popularity contest.
http://en.wikipedia.org/wiki/Entropy
> You can put work into a system to reestablish an energy differential.
Yes, but that doesn't change the definition of entropy -- it just borrows energy from somewhere else.
Why link me to the Wikipedia article or insinuate I'm pulling this out of--to put it more politely--ex culo? Given my use of notation, one might assume I am at least a little familiar with how the thermodynamic entropy functions are mathematically derived.
To be pedantic for a bit, Entropy is an abstract mathematical state function useful for the prediction of thermodynamic systems. Much like the Gibbs and Helmholtz terms, entropy has no direct qualitative basis; there are many open-ended interpretations seeking to justify what it means, which is not unlike looking for God or faeries or what have you.
Mathematically speaking, I think you got your equality / definition wrong. Which energy function do you refer to? If you are still convinced about an error on my part, you can demonstrate in classical thermodynamics that,
S = "the inverse of available energy to do anything"
What's my incentive to continue a discussion with someone who has abandoned the topic? In a closed system, the amount of exploitable energy, and the quantity called entropy, move in opposite directions.
> ... or insinuate I'm pulling this out of--to put it more politely--ex culo?
Point to where I said this. If you can't, then you have abandoned the topic.
> Much like the Gibbs and Helmholtz terms, entropy has no direct qualitative basis; there are many open-ended interpretations seeking to justify what it means, which is not unlike looking for God or faeries or what have you.
Nonsense. Entropy is clearly understood, it's not a philosophical puzzle as you suggest. It's easily quantifiable. It's science, not philosophy.
> Given my use of notation, one might assume I am at least a little familiar with how the thermodynamic entropy functions are mathematically derived.
Anyone can adopt the notations used in science. This doesn't tell me anything about their knowledge of the topics under discussion. You simultaneously apply standard terminology, but you go on to say that explaining entropy is "not unlike looking for God or faeries or what have you", which means you don't understand the significance of the symbols you used.
Entropy = k log(n)
k = Boltzmann's constant.
n = number of states the system can be in.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.ht...
Quote: "Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general."
Yeah, but physics aren't a la carte. Either prove it wrong (and get a nobel) or accept it.